Continuous casting method and apparatus thereof

ABSTRACT

A continuous casting method and apparatus therefor wherein a reaction force/reduction controller selects a pivot reduction roll such that the thickness of the solidified shell of the cast slab having a liquid core is equal to the target thickness T ref , and calculates a difference between a thickness T in  of the cast slab having a liquid core at the inlet of the reduction roll zone PRT and the target thickness T ref , i.e., ΔT. The resulting value of ΔT, i.e., a target reduction is provided to the reduction controllers 2 of the pivot reduction roll. The reaction force/reduction controller 1 assigns target reductions 1/3 ΔT and 2/3 ΔT to the two reduction rolls upstream of the pivot reduction roll. The reaction force/reduction controller 1 calculates a target pressure (P i  +α) on the basis of the selected value for α, and the resulting target pressure (P i  +α) is provided to each of the reduction controllers 2 of the reduction rolls, downstream of the pivot reduction roll.

TECHNICAL FIELD

The present invention relates to a continuous casting method and anapparatus therefor in which a cast slab is continuously withdrawn from amold, and more particularly one in which a cast slab having a liquidcore is subjected to reduction so as to produce a thin cast slab.

BACKGROUND ART

A typical method of producing a thin plate includes rolling and formingin a rolling step. In this type of method, it is necessary beforeapplication of hot rolling to reheat a cast slab which has once cooledafter casting. This process is disadvantageous from the viewpoint ofenergy consumption.

Recently, a direct hot rolling method has been under development.According to the direct hot rolling method, a cast slab obtained from acontinuous casting machine is directly supplied to a rolling mill.Particularly, many attempts have been made to develop a continuouscasting method which can produce cast slabs with rough hot rolling beingomitted in the direct hot rolling process.

As a method of producing a thin cast slab, there has been proposed amethod comprising continuously withdrawing a cast slab out of the mold,reducing the thickness of the cast slab using a plurality of pairs ofreduction rolls while it has a liquid core, and cooling the resultingslab. This method is referred to as the liquid core reduction method.

Japanese Patent Publication No. 6-28790/1994 discloses a method ofreducing the thickness of cast slabs having a liquid core with pairs ofreduction rolls. According to this method, a series of spacers eachhaving a different thickness are inserted between each pair of rolls toproduce a cast slab having a target thickness by means of an arrangementin which the thickness of spacers gradually increases for downstreampairs of rolls and the roll gaps between the pair of rolls graduallydecrease for downstream pairs of rolls. Cast slabs are subjected to areduction force corresponding to roll gaps in each of which spacers areinserted. In addition, Japanese Patent Publication No. 6-28789/1994discloses a method of carrying out casting by applying to each pair ofrolls a reduction force which is increased depending on the timerequired until an unsolidified cast slab withdrawn from a mold reachesrespective reduction rolls so that a given amount of roll reduction maybe applied to the cast slab before finishing the roll reduction.

SUMMARY OF THE INVENTION

According to the prior art method disclosed in Japanese PatentPublication No. 6-28790/1994, however, a roll gap, which determines thethickness of cast slabs, is determined by spacers, and many spacers mustbe stored in order to produce a wide variety of thickness of slabs.Spacers must be changed every time the thickness of cast slab ischanged. Thus, this method is not practical. In addition, since thereaction force of the roll reduction is not considered, a problem ofvariation with respect to thickness of cast slabs is inevitable.

On the other hand, since cast slabs have different densities dependingon their steel types, a reaction force is also varied. According to theprior art method disclosed in Japanese Patent Publication No.6-28789/1994, the reduction force is determined by a time interval untila cast slab withdrawn from a mold reaches a reduction roll. Thus, thereis a problem that variation in the thickness of cast slabs, which iscaused by a change of the reaction force to each of the reduction rolls,cannot be entirely prevented.

In addition, in either method, reduction of roll gaps is described, butthere is no description of the case where the roll gap is increased. Theamount of strains introduced in the solidification interface during rollreduction of cast slabs having a liquid core is determined depending onthe amount of reduction of the liquid core, but not on the reductionspeed of the reduction rolls. Thus, however much the reduction speed isincreased, there is no internal cracking occurring during roll reductionof a liquid core until a target reduction of the liquid core is achievedas long as the target reduction is within a range where the cast slab isfree from internal cracking. However, in the case of releasing rollreduction of a liquid core, i.e., in the case of increasing a roll gap,internal cracking sometimes occurs when the rate of increase of the rollgap is over a certain amount.

An object of the present invention is to provide a continuous castingmethod and an apparatus for carrying out the method, according to whichcast slabs having a desired thickness can be produced with greatprecision, and also cast slabs having a uniform internal structure freefrom segregation of impurities in the central area of the slabs can beproduced.

Another object of the present invention is to provide a continuouscasting method and an apparatus therefor, in which cast slabs free frominternal cracking having a uniform internal structure can be producedwith great precision even when the roll gap is increased or decreased.

The present invention is a process for continuously casting slabs, whichcomprises supplying cast slabs continuously withdrawn from a mold to aplurality of reduction devices arranged in tandem, providing a targetroll gap, i.e., a roll reduction or target pressure to each of thereduction device, and performing roll reduction of a liquid core withthe target roll gap and target pressure capable of being achieved foreach of the reduction devices, characterized by selecting one of theplurality of reduction devices as a pivot reduction device, providing(assigning) a target roll gap to the pivot reduction device and each ofthe apparatuses upstream thereof, and providing (assigning) a targetreduction force to each of the reduction devices downstream of the pivotreduction device. Thus, according to the present invention, when a rollgap is decreased, a target roll gap is set so that the thickness of castslabs is smaller than the thickness of the mold. On the other hand, whenthe thickness of cast slabs is changed to be larger than before duringcontinuous casting, i.e., when the roll gap increases, the thickness ofcast slabs being subjected to reduction of a liquid core is restored toa target valve which is equal to or smaller than that of a mold.

In another aspect, the present invention is a continuous castingapparatus in which cast slabs continuously withdrawn from a mold aresupplied to a plurality of reduction devices arranged in tandem, atarget roll gap or target pressure is provided (assigned) to each of thereduction device, and roll reduction of a liquid core with the targetroll gap or target pressure being able to be achieved for each of thereduction devices is performed, characterized by comprising a means ofselecting any one of the plurality of reduction devices as a pivotreduction device, means for providing (assigning) a target roll gap tothe pivot reduction device and each of the apparatuses upstream thereof,and means for providing (assigning) a target reduction force to each ofthe reduction devices downstream of the pivot reduction device. Theapparatus of the present invention further comprises means for providinga roll gap smaller than the thickness of the mold based on the means forproviding a target roll gap, when a roll gap is decreased, i.e., castslabs having a thickness smaller than that of the mold are produced. Onthe other hand, the apparatus of the present invention further comprisesmeans for providing a roll gap larger than that being used, based onsaid means for providing a target roll gap, when the roll gap increases,i.e., when the thickness of cast slabs is changed to be larger thanbefore during continuous casting (hereunder sometimes merely referred toas "release of roll gap").

Thus, according to the present invention, a cast slab continuouslywithdrawn from a mold with a solidified shell surrounding a liquid coreis supplied to a plurality of reduction devices arranged in tandem. Asthe cast slab goes downstream toward the reduction device, the cast slabis cooled, and an unsolidified portion thereof is gradually solidifiedwith an increase in thickness of the solidified shell. A position of acast slab from the mold where the thickness of the solidified shellreaches a target one is calculated, for example, by using equation (2)to be described later or based on the thermal conductivity in a mannerdescribed in FIG. 13 to be explained later. A reduction device which isdisposed at a position closest to the calculated position of the castslab is selected as a pivot reduction device.

When the roll gap is decreased, a predetermined pivot reduction deviceis provided with a roll gap corresponding to a difference between thethickness of the cast slab at the exit of the mold and a targetthickness thereof and each of the reduction devices upstream of thereference one is provided with a target roll gap calculated bymultiplying the difference by a certain ratio so that cast slabs can bereduced with respect to their thickness gradually at an appropriateproportion through a first half group of the reduction devices includingthe pivot reduction device. It is possible, therefore, to set anydesired target thickness, i.e., roll gap, and to carry out reduction toobtain such a predetermined target thickness of cast slabs.

In addition, each reduction device downstream of the pivot reductiondevice is provided with a target pressure calculated on the basis of areaction force previously determined based on the type of steel and onan iron static pressure of the cast slab at the position of thecorresponding reduction device. Reduction through a second half group ofreduction devices is carried out so that the target pressure can bemaintained in each of the reduction devices. The iron static pressurecan be calculated based on the density of the cast slab, a height fromthe reduction device to a meniscus, etc. The reaction force can be set,as described before, depending on the type of cast slab. It is possible,therefore, to prevent occurrence of a variation of thickness of castslabs, which is sometimes caused by assignment of an unsuitable reactionforce to a cast slab.

Thus, according to the present invention, a target roll gap is assignedto the pivot reduction device and a first group of reduction devicesupstream thereof, and a target pressure is assigned to a second group ofreduction devices downstream of the pivot reduction device. It ispossible to perform roll gap control and roll pressure controlsimultaneously to produce thin cast slabs having a predeterminedthickness free from a variation in thickness which is caused byassignment of an unsuitable reaction force.

On the other hand, when the thickness is to be increased duringoperation, a reduction device which is used as the reference one beforeis taken as the pivot reduction device. The pivot reduction device isprovided with a target roll gap corresponding to a difference betweenthe thickness of the cast slab after reduction in the precedingoperation, i.e., the present roll gap, and a new target thicknessthereof, and the reference reduction and each of the reduction devicesupstream of the reference one as provided with an increased target rollgap calculated by multiplying the difference by a certain ratio so thatcast slabs can be reduced with respect to their thickness gradually atan appropriate proportion through a first group of the reduction devicesincluding the pivot reduction device. It is possible, therefore, to setany desired target thickness, i.e., roll gap, and to carry out reductionto obtain cast slabs having an increased target thickness.

In addition, in the same manner as before, each of the reduction devicesdownstream of the reference device is provided with a target pressurecalculated on the basis of a reaction force previously determined basedon the type of steel and the iron static pressure of the cast slab atthe position of the corresponding reduction device.

In either case of increasing or decreasing a roll gap, the targetpressure is set to be larger than the iron static pressure by a certaindegree. Thus, it is possible to reduce the thickness of cast slabs at atarget pressure for each of the reduction devices downstream of thepivot reduction device without release of reduction due to the ironstatic pressure during operation to increase the thickness of castslabs.

The iron static pressure can be calculated based on the density of thecast slab, the height from the reduction device to a meniscus, etc. Thereaction force can be set, as described before, depending on the type ofsteel. It is possible, therefore, to prevent variation in the thicknessof cast slabs, which is sometimes caused by assignment of an unsuitablereaction force to a cast slab.

Thus, according to the present invention, even when the thickness isincreased during operation, a target roll gap is assigned to the pivotreduction device and the first group of reduction devices upstream ofthe pivot reduction device, and a target pressure is assigned to thesecond group of reduction devices downstream of the pivot reductiondevice. It is possible to perform roll gap control and roll pressurecontrol simultaneously to produce thin cast slabs having a predeterminedthickness free from a variation in thickness which is caused byassignment of an unsuitable reaction force.

In the case of either an increasing or decreasing roll gap, thethickness of a cast slab at the exit of the pivot reduction device isdetermined on the basis of a value detected by a thickness meter, or onthe basis of a roll gap of the reduction device next to the pivotreduction device on the downstream side. When the determined thicknessis smaller than the target thickness, it is judged that the thickness ofthe unsolidified portion of the slab is excessively large, and in placeof the present pivot reduction device, the reduction device next to thepivot reduction one on the downstream side is made a new pivot reductiondevice. In addition, the roll gap is detected for the pivot reductiondevice. When the detected roll gap is larger than a difference betweenthe thickness of the cast slab withdrawn from the mold and a targetthickness, it is judged that the thickness of the unsolidified portionof the slab is excessively large, and in place of the present pivotreduction device, the reduction device next to the pivot reduction oneon the upstream side is made a new pivot reduction device. Thus,according to the present invention, a pivot reduction device is alwayssuitably selected.

In case of either an increasing or decreasing roll gap, in the pivotreduction device and the reduction devices upstream of the pivotreduction device, the direction of pressure applied to a hydraulicdouble-acting cylinder is determined based on whether the valuesdetected by the roll gap detector and a difference from the target rollgap are positive or negative. In addition, a pressure corresponding tothe difference may be made a target pressure, and the degree of openingof a pressure control valve can be adjusted on the basis of the targetpressure and a value detected by a pressure meter. The pressure controlvalve is operated such that a predetermined degree of opening isachieved, and the switching valve is operated such that a predetermineddirection of pressure is achieved. Thus, the roll gap of each of thereduction devices can be adjusted to respective target roll gaps byoperating the switching valve and pressure control valve.

In the reduction devices downstream of the pivot reduction device, thedegree of opening of the pressure control valve is determined on thebasis of an assigned target pressure and a pressure detected by apressure gauge, and pressure control is carried out by adjusting thepressure control valve so as to achieve the determined degree ofopening.

It is necessary to prevent occurrence of internal cracks of cast slabswhen a roll gap must be increased, i.e., when the thickness of castslabs must be increased. In such situations, the present inventionprovides a continuous casting method for producing thin cast slabs byapplying liquid core reduction in a roll reduction zone, characterizedin that the roll reduction force is released in such a way that a rateof increase of the final roll gap is satisfied by the followingequation, which determines the target roll gap, when the thickness ofcast slabs is returned to a thickness smaller than the originalthickness of the cast slab before application of roll reduction.##EQU1## wherein V_(R) : raising rate of the reduction roll (mm/S)

V_(C) : casting speed (m/min)

L: minimum roll pitch, i.e., minimum distance from one roll to the nextroll in the roll reduction zone (mm)

L_(S) : length of roll reduction zone (m)

ε_(Cr) : critical strains of internal cracks of cast steel (%)

D: maximum solidified shell thickness at the exit of a liquid reducingroll (mm)

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration of a bent-type continuous castingmachine for producing slabs of the present invention.

FIG. 2 is a diagrammatic illustration of a control system for a drivemechanism of a reduction device.

FIG. 3 is a sectional side view of a cast slab having a liquid corewhich is supplied to a roll reduction zone.

FIG. 4 is a block diagram showing a control logic for a pivot reductionroll and reduction rolls upstream thereof.

FIG. 5 is a block diagram showing a control logic for reduction rollsdownstream of the pivot reduction roll.

FIGS. 6a, 6b, and 6c are flow charts describing processes forcalculating a target roll gap and a target pressure, and for determininga pivot reduction roll, respectively.

FIG. 7 is a diagrammatic illustration of a reduction device for castslabs having a liquid core, which is employed by the present invention.

FIG. 8 is an illustration showing the occurrence of clearance betweenthe cast slab and supporting rolls during releasing roll reduction.

FIG. 9 is an illustration showing the occurrence of bulging deformationcaused by clearance between the cast slab and supporting rolls duringreleasing roll reduction.

FIG. 10 is a graph showing the amount of bulging as a function of timeduring releasing roll reduction.

FIGS. 11a through 11f are diagrammatic views showing releasing strainsintroduced into a cast slab having a liquid core by roll reduction whilea portion of maximum bulging of the cast slab is passing from onesegment of the roll reduction zone to the next segment.

FIG. 12 is a graph showing the maximum amount of bulging db as afunction of casting speed Vc for different reduction releasing speedsV_(R).

FIGS. 13a and 13b are graphs showing results obtained by calculating thethickness of a solidified shell based on thermal conductivity.

FIG. 14 is a graph showing the thickness of a solidified shell and thethickness of a liquid core with respect to time at the position of thepivot reduction roll.

FIG. 15 is a graph showing results of a simulation of changing roll gappatterns during control of a roll gap.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention will be explained in further detailwith reference to the accompanying drawings.

FIG. 1 is a diagrammatic illustration of a bent-type continuous castingmachine for producing slabs. In the figure, a ladle L in which a moltensteel is contained is moved to above a tundish T. At the bottom of theladle L a sliding nozzle SN is provided. When the sliding nozzle isopened, a molten steel within the ladle L is passed into the tundish Tand stored therein temporarily.

At the bottom of the tundish T, a feed nozzle FN is disposed and extendsinto a mold M having a shape of a rectangular barrel. A molten metalintroduced into the tundish T is kept there temporarily, and then themolten steel is poured into the mold M as a stable flow via the feednozzle FN. The molten steel poured into the mold is cooled and withdrawnfrom the mold as cast slabs having a solidified shell surrounding aliquid core. Downstream of the mold M is provided a spray roll zonewhere cooling water is sprayed at the cast slab. In the spray roll zone,an unsolidified portion of the cast slab is further cooled (secondarycooling). Following the spray roll zone SR, a plurality of groups ofroll zones GR₁, GR₂, GR₃, GR₄, and GR₅, and a pinch roll zone PIR arearranged with a prescribed curvature so as to bend the cast slabs havinga liquid core while moving them to a horizontal position. Cast slabshaving a liquid core are disposed horizontally and then passed to areduction roll zone PRT where the cast slabs are reduced with respect totheir thickness by means of a plurality of reduction rolls PR which arearranged in tandem, and then further cooled while roll reduction iscarried out to continuously produce cast slabs.

Each of the reduction rolls PR, PR, . . . is connected to a rod 5 of apiston 4 provided in a hydraulic cylinder 3. A reduction roll PR,hydraulic cylinder 3, and piston rod 4 make up a reduction device. Aplurality of reduction controllers 2, each of which controls reductionmovement of each of the reduction devices are provided with a targetpressure or target roll gap form a reaction force/roll gap controller 1.The positions of pistons 4 and the pressure of cylinders 3 arecontrolled such that each of the reduction controller 2 is provided withan assigned target pressure or target reduction position.

FIG. 2 is a diagrammatic illustration of a control system for driving areduction device. Each of the reduction rolls PR has an upper roll 15and a lower roll 16. Above the upper roll 15, double-acting hydrauliccylinders 3 are disposed with rods 5 of pistons 4 facing downward. Thelower ends of the rods 5 are connected to respective ends of the upperroll 15. The upper roll 15 is provided with a predetermined roll gap orreduction pressure using the hydraulic cylinders 3, so the thickness ofa cast slab S having a liquid core is reduced when it passes through theroll gap between the upper and lower rolls 15, 16.

The hydraulic cylinder 3 comprises upper and lower chambers divided by apiston 4, and hydraulic piping 17, 18 connected to the chambers at oneend thereof. At its other end, piping 17 is connected via a motor-drivenpressure control valve 10 to one port of a magnetic switching valve 8 ofthe 4 port-2 position type. Piping 18 is connected to another port ofthe switching valve 8. One of the remaining two ports of the switchingvalve 8 is connected via a pump P to an oil tank 7, and the other one isdirectly connected to the oil tank 7. The pressure control valve 10 isprovided with piping 19 so as to return excess oil to the oil tank 7during time period of reducing pressure. When the switching valve 8 isoperated to supply oil to one of the tow chambers of the hydrauliccylinder 3, the piston 4 is moved upward or downward. The oil pressurewithin the hydraulic cylinder 3 is adjusted by the pressure controlvalve 10. The hydraulic cylinder 3 has a roll gap detector 6. A roll gapdetected by the detector 6 is provided to a reduction controller 2. Apressure meter 12 is disposed between the pressure control valve 10 ofthe piping 17 and the hydraulic cylinder 3 to detect the oil pressurewhich has been adjusted by the pressure control valve 10. A signalcorresponding to the pressure detected by the pressure meter 12 isprovided to the reduction controller 2. As described before, thereduction controller 2 is provided with a target pressure and targetroll gap from the reaction force/roll gap controller 1 (see FIG. 1), andthe reduction controller 2 provides signals to change the opening or theposition of the pressure control valve 10 and the switching valve 8,respectively, so that the detected values of the pressure meter 12 andthe roll gap detector 6 will be the same as the target pressure and thetarget roll gap.

Although the above explanation pertains to one of the cylinders 3, thesame explanation applies to the other cylinder 3.

The reaction force/reduction controller 1 can determine a targetreduction pressure and a target roll gap in the following manner.

FIG. 3 is a sectional side view of a cast slab 30 having a liquid corewhich is supplied to a roll reduction zone PRT. The cast slab 30supplied to the roll reduction zone PRT is cooled by air, and thethickness of a liquid core S_(G) remaining in the center of the slabdecreases gradually, and simultaneously, the thickness of a solidifiedshell S_(S) surrounding the liquid core S_(G) increases. At a finalstage, the liquid core S_(G) of the cast slab disappears.

A pivot reduction roll PR₀ is selected from a plurality of reductionrolls PR, PR, . . . in the reduction roll zone PRT of the reactionforce/roll gap controller 1 in accordance with the following equations(1) and (2). Namely, the pivot reduction roll PR₀ is made the reductionroll which is closest to the position where the sum of the thickness T₁of the solidified shell S_(S) on the liquid core S_(G) of the cast slaband the thickness T₂ of the solidified shell S_(G) underneath the liquidcore S_(G), i.e., T₁ +T₂, is equal to a target thickness T_(ref).

    T.sub.i =k√(L.sub.e /V.sub.C)=T.sub.ref             (1)

    L.sub.e =(T.sub.ref /k).sup.2 V.sub.C                      (2)

wherein

T_(i) : thickness of a solidified shell

    T.sub.i =T.sub.1 +T.sub.2

k: solidification coefficient obtained based on thermal conductivity (mmmin^(-1/2))

L_(e) : distance from the meniscus to the reduction roll (m)

V_(C) : casting speed (m/min)

In another embodiment, the position of the pivot reduction roll can bedetermined by calculation based on thermal conductivity. See thedescriptions relating to FIG. 13.

When a roll gap, i.e., a roll reduction is decreased, after determiningthe pivot reduction roll PR₀, the reaction force/reduction controller 1provides a reduction controller for the selected pivot reduction rollPR₀ with a target reduction, which is equal to the difference ΔT betweenthe thickness T_(in) of the cast slab at the inlet of the roll reductionzone, i.e., the thickness of the mold, and a target thickness T_(ref)(ΔT=T_(in) -T_(ref)).

The reaction force/reduction controller 1 also provides targetreductions obtained by multiplying the difference ΔT by predeterminedratios for a certain number of reduction rolls PR₋₁, PR₋₂, . . .upstream of the pivot reduction roll PR₀. For example, when tworeduction rolls PR₋₁ and PR₋₂ upstream of the pivot reduction roll PR₀are controlled, a target pressure or reduction corresponding to areduction of 1/3 ΔT is assigned to the reduction controller forreduction roll PR₋₁, and a value of 2/3 ΔT is assigned to reduction rollPR₋₂.

The amounts of 1/3 ΔT, 2/3 ΔT, and Δt are indicated by S₀. The reductioncontroller 2 can be controlled by the following manner based on S₀.

FIG. 4 is a block diagram showing control logic for the pivot reductionroll and reduction rolls upstream thereof. The signal S₀ is provided toa first subtractor 21 of each of reduction controller 2 which controlthe pivot reduction roll and the reduction rolls upstream thereof. Tothe first subtractor 21, reduction data detected by the reductiondetector 6 are also provided, and the first subtractor 21 outputs avalue obtained by subtracting the detected reduction from S₀ to apressure signal control unit 22. The first subtractor 21 provides theresult of subtraction to a switching signal control unit 25. Theswitching signal control unit 25, depending on whether the resultingdata are positive or negative, determines a direction of movement of thepiston of the cylinder 3, forms a switching signal, and provides it tothe switching valve 8.

The before-mentioned pressure signal control unit 22 calculates by PIDcalculation a pressure signal corresponding to a difference from apredetermined reduction and provides the signal to a second subtractor23. To the second subtractor 23, a hydraulic pressure which is adjustedby a pressure control valve 10 is supplied from the pressure meter 12.The second subtractor 23 outputs the difference between the pressuresignal and hydraulic pressure to the opening signal control unit 24. Theopening signal control unit 24 calculates an opening signalcorresponding to the difference by PID calculation and provides theresult to the pressure control valve 10 to adjust the degree of openingand to control the reduction.

The reaction force/reduction controller 1 shown in FIG. 1, as shown inFIG. 3, provides a substantial reaction force α and a target pressure(P_(i) +α) obtained from the following equation (3) to the reductioncontrollers 2 of the reduction rolls PR₁, PR₂, . . . downstream of thepivot reduction roll PR₀. The substantial reaction force α is varieddepending on the type of steel, and the reaction force/reductioncontroller 1 stores specific values of α for respective types of steel.

    P.sub.i =(P.sub.0 ×S)/A                              (3)

wherein

P₀ : iron static pressure

    P.sub.0 =ρ g h

wherein:

ρ: density of molten metal

g: acceleration of gravity

h: height of the molten metal level within tundish from a reduction roll(m)

S: contact surface between roll and cast slab

    S=r.sub.p ×{W-(T.sub.1 +T.sub.2)}

wherein

r_(p) : roll pitch

W: width of mold

A: sectional area of the cylinder

FIG. 5 is a block diagram showing a control logic for reduction rollsdownstream of the pivot reduction roll PR₀. The reaction force/reductioncontroller 1 has an α table 32 which includes data of α respective for avariety of steels. A target pressure calculating unit 31 reads the dataof α for the steel being processed from the α table 32, calculates thetarget pressure (P₁ +α) in accordance with equation (3), and providesthe resulting data to a subtractor 26 of the reduction controller 2which controls the reduction rolls downstream of the pivot reductionroll. To the subtractor 26, the hydraulic pressure which is supplied tothe hydraulic cylinder 3 is provided by the pressure meter 12. Thehydraulic cylinder 3 is operated at a force f determined in accordancewith the following equation (4). The subtractor 26 provides a differencebetween the target pressure (P_(i) +α) and a hydraulic pressure detectedby the pressure meter 12 to the opening signal control unit 27.

    f=(P.sub.1 +α)×A                               (4)

The opening signal control unit 27 generates an opening signalcorresponding to the determined difference and provides it to a pressurecontrol valve 10 to adjust the degree of opening so that the reductionby the hydraulic cylinder 3 can be controlled. Thus, a reductioncorresponding to the reaction force is applied to the cast slab, andcast slabs having a target thickness can be produced with highprecision.

Since the pivot reduction roll PR₀ is determined by the before-describedcalculation, which inevitably includes errors, due to the presence ofsuch errors, the thickness of a liquid core is sometimes larger orsmaller than ΔT. The reaction force/reduction controller 1 can shift theposition of the pivot reduction roll PR₀ as follows.

In FIG. 3, on the basis of a reduction detected by the reductiondetector 2 (see FIG. 2) which is provided on the reduction roll PR₁ nextto the pivot reduction roll PR₀ on the downstream side, the distancebetween the upper and lower rolls of this reduction roll PR₁ isdetermined. This distance is the thickness T_(out) at the exit of thepivot reduction roll PR₀. When T_(out) <T_(ref), i.e., the thickness ofthe liquid core is larger than ΔT, the reaction force/reductioncontroller 1 changes the position of the pivot reduction roll PR₀ to theone immediately downstream of the previous pivot reduction roll. Thereaction force/reduction controller 1 repeatedly determines T_(out) andshifts the position of the pivot reduction roll until T_(ref) -T_(out)=0.

When the thickness of a liquid core is larger than ΔT, since the actualreduction at the pivot reduction roll PR₀ is ΔT-α and a large reactionforce is produced, the reaction force/reduction controller 1, based onthe reduction detected by the reduction detecting device 6 disposed onthe pivot reduction roll PR₀, shifts the position of the pivot reductionroll PR₀ to the roll just upstream of the previous pivot reduction rollfi the actual reduction is equal to ΔT-α. The reaction force/reductioncontroller 1 repeatedly shifts the position of the pivot reduction rollPR₀ until the actual reduction is equal to ΔT.

When the position of the pivot reduction roll PR₀ is changed, thereaction force/reduction controller 1 provides a target reduction and atarget pressure which can result in the same reduction as thatpreviously determined to the reduction rolls PR₋₁, PR₋₂, . . . upstreamof the pivot reduction roll PR₀ after correction, and to the reductionrolls PR₁, PR₂, . . . , downstream of the pivot reduction roll PR₀.

In order to select the pivot reduction roll, either of the followingmethods may be used. One method is to select it in accordance with aroll reduction detected by a series of steps S1 through S12 shown inFIG. 6a through FIG. 6c, and the other is to select it on the basis ofreaction forces.

FIGS. 6a through 6c are flow charts describing processes for calculatinga target roll reduction and a target pressure and for selecting thepivot reduction roll in the reaction force/reduction controller 1.

The reaction force/reduction controller 1 is provided with a targetthickness T_(ref) of cast slabs. A pivot reduction roll PR₀ is selectedfrom the reduction rolls of the reduction roll zone PRT in accordancewith the before-described equations (1) and (2) such that the thickness(T₁ +T₂) of the solidified shell S_(S) of the cast slab having a liquidcore is equal to the target thickness T_(ref) (Step S₁).

The reaction force/reduction controller 1 is also provided with data ofsubstantial reaction force α for each type of steel, and the reactionforce/reaction controller 1 chooses a specific value of α for the steelbeing processed (Step S₂). After the pivot reduction roll PR₀ isselected, the reaction force/reduction controller 1 calculates adifference between a thickness T_(in) of the cast slab having a liquidcore at the inlet of the reduction roll zone PRT and the targetthickness T_(ref), i.e., ΔT=T_(in) -T_(ref) (Step S₃). The resultingvalue of ΔT, i.e., a target reduction is provided to the reductioncontrollers 2 of the pivot reduction roll PR₀ (Step S₄). The reactionforce/reduction controller 1 assigns target reductions calculated bymultiplying the difference ΔT by 1/3 and 2/3, respectively, i.e, 1/3 ΔTand 2/3 ΔT to the two reduction rolls upstream of the pivot reductionroll PR₀ (Steps S₃, S₄).

The reaction force/reduction controller 1 calculates a target pressure(P_(i) +α) on the basis of the selected value for α and thebefore-described equation (3) (Step S₅), and the resulting targetpressure (P_(i) +α) is provided to each of the reduction controllers 2of the reduction rolls PR₁, PR₂, . . . downstream of the pivot reductionroll PR₀. (Step S₆).

The reaction force/reduction controller 1 reads detected data of thereduction detectors 6 fixed to the reduction roll PR₁ downstream of thepivot reduction roll PR₀ (Step S₇). the distance between the upper andlower rolls of the reduction roll PR₁, which is detected by thereduction detector 6, is taken as the thickness T_(out) at this exit ofthe pivot reduction roll PR₀ (Step S₈). The reaction force/reductioncontroller 1 decides whether T_(out) ≧T_(ref) (Step S₉). When theinequality T_(out) ≧T_(ref) is not satisfied, the reactionforce/reduction controller 1 decides to shift the position of the pivotreduction roll PR₀ to the next roll downstream (Step S₁₀)and returns toStep S₃. See FIG. 6a. This process is repeated until the inequalityT_(out) ≧T_(ref) is satisfied in Step S₉.

When it is determined that the inequality T_(out) ≧T_(ref) is satisfiedin Step S₉, the reaction force/reduction controller 1 decides whetherthe actual reduction is equal to ΔT on the basis of the detected data ofthe reduction detector 6 fixed to the pivot reduction roll PR₀ (StepS₁₁). If it is not equal to ΔT, the pivot reduction roll PR₀ is made thenext roll upstream at the time when the detected data reach ΔT-α (StepS₁₂), and Step S₃ is returned to. This process is repeated in thereaction force/reduction controller 1 until it is decided that theactual reduction is equal to ΔT in Step S₁₁.

Alternatively, as shown in FIG. 6c, if it is judged that the reactionforce of the pivot reduction roll is larger than the presetting pressure(P_(o) ˜P_(oo)), i.e., P_(o) <, the present position of the pivotreduction roll is unsuitable, so the position is shifted to the nextroll upstream. When the reaction pressure is within the range of P_(o)˜P_(oo), it is decided that the position of the pivot reduction roll issuitable. In contrast, if the roll reduction is finished at a pressuresmaller than the preset value, it is decided that the position of thepivot reduction roll is not suitable, and the position is shifted to thenext roll downstream.

The explanation above has been made with reference to the case in whichthe thickness of the cast slab is reduced. When it is necessary toincrease the thickness of the cast slab, e.g., when the thickness oncereduced is to be increased, or when the thickness once reduced is to berestored to its starting one, the target thickness T_(out-1) beforechange must be increased to a new target thickness T_(out-2), whereT_(out-2) ≦T_(in).

In this case, the pivot reduction roll PR₀ before change is decided tobe used as a new pivot reduction roll, and a reduction controller forthe reaction force may provide an increase of reduction by a differencebetween the solidified shell thickness T_(out-1) of the present castslab and an increased target thickness T_(out-2), i.e., ΔT₂ =T_(out=2)-T_(out-1) to the reduction controller of the pivot reduction roll PR₀.

In addition, the reaction force/reduction controller calculates newtarget reductions each having an increase obtained by multiplying thebefore-described difference ΔT₂ by a given ratio, and provides them toeach of a predetermined number of reduction rolls PR₋₁, PR₋₂, . . .upstream of the pivot reduction roll PR₀. When two reduction rolls PR₋₁and PR₋₂ upstream of the pivot reduction roll PR₀ are to be controlled,for example, the reduction controller of reduction roll PR₋₁ is providedwith a target pressure and reduction having an increase of 1/3 ΔT₂, andthe reduction controller of reduction roll PR₋₂ is provided with atarget pressure and reduction having an increase of 2/3 ΔT₂.

Thus, if 1/3 ΔT₂, 2/3 ΔT₂, or ΔT₂ is taken as S₀, the reductioncontroller 2 can be controlled using the value of S₀ in accordance withthe control logic which is applicable to the pivot reduction roll andreduction rolls upstream thereof, as shown in FIG. 4, for example.Furthermore, control of reaction force during reduction for thereduction rolls PR_(i) downstream of the pivot reduction roll PR₀ andcorrection of the position of the pivot reduction roll can be done inthe same manner as in the case of reduction of thickness.

In the embodiments described before, the reduction device is of theoil-actuated type, but in accordance with the present invention, inplace of oil, other mediums may be used.

In addition, the reduction device is actuated by a cylinder, but a screwjack, for example, may be used.

There are a variety of means of carrying out reduction of cast slabshaving a liquid core. Thus far the present invention has been describedwith reference to a case in which invention has been described withreference to a case in which each of the reduction rolls isindependently controlled with respect to its reaction force orreduction. As shown in FIG. 7, as a cheaper and easily operated deviceto control reduction more precisely, there is proposed a devicecomprising segmented frames each having cast slab supporting rolls 40 inthe roll reduction zone PRT, one of the frames being a movable frame 41which is movable in the direction of the cast slab, and the other framebeing a fixed frame 42. The movable frame 41 can be made to slope byhydraulic devices 43 to effect reduction. In the illustrated case, twohydraulic pressure means are used to control the reduction performed byrolls R₁ to R₅.

When liquid core reduction is carried out, the inner quality of theresulting cast slab is not adversely affected. However, when release ofthe reduction is carried out, the inner quality of the resulting castslab is sometimes degraded.

Namely, the amount of strains introduced at the solidification interfaceduring reduction of a cast slab having a liquid core is determined onlyby the amount of reduction, not by the reduction rate. As long as theamount of reduction is so small that no internal cracks occur, even ifthe reduction rate is increased to any degree, there will be no internalcracks during reduction to a target thickness. On the other hand, in thecase of increasing a roll gap, if a releasing speed of the reduction isincreased beyond a certain point, strains are newly introduced, causinginternal cracks in accordance with the following mechanism.

The arrangement shown in FIG. 7 in which segmented reduction rolls areemployed will be used as an example. According to the embodiment shownin FIG. 8, when the reduction is released, reduction rolls fixed to themovable frame 41 are moved away from the cast slab SB. When the castslab contacting a roll j at a time t(i) moves to a roll j+1at a timet(i+1), a clearance 45 will be formed between the cast slab and the rollat the position of roll j+1 if a roll gap G (j+1, i+1),i.e., theshortest distance between the roll surfaces of the rolls on movableframe 41 and the fixed frame 42 for the roll j+1 at time t(i+1) islarger than the thickness of the cast slab at time t(i), i.e., the rollgap G (j, i) of roll j at time t(i).

The clearance 45 first occurs at the exit roll of the segmented rolls,and it spreads to upstream rolls.

FIG. 9 illustrates the shape of a cast slab during release of reduction,in which a solidified shell S_(S) receives a static pressure from aunsolidified portion S_(G), and at the position of the slab supportingroll PR, a deformation 46 due to bulging occurs to occupy the clearance.The deformation caused by bulging is hereunder called "bulgingdeformation" in order to distinguish it from general bulging occurringbetween rolls. The amount of bulging deformation can be defined by thedifference (db) between the roll gap and a thickness of the cast slab atthe edge portions thereof.

FIG. 10 shows the bulging deformation at the exit of the segmentedreduction rolls when release of reduction of a cast slab having a liquidcore is carried out using segmented rolls comprised of 5 supportingrolls, as in FIG. 7. The bulging deformation occurs during the secondhalf of release of reduction. The maximum is reached at the end ofrelease of reduction. The time when the release of reduction is finishedis the point when an unsolidified portion disappears and the roll gap atthe exit of the segmented rolls reaches a target thickness. In the caseillustrated in FIG. 10, it was 50 seconds after the release was started.After the completion of release, the bulging deformation remains untilthe thickness of the edge portions of the slab reaches a target value,e.g., 90 mm in the case of FIG. 10. The distance the cast slab passes ina time period from the beginning of the bulging deformation to theattainment of the maximum level thereof is equal to the length L_(S) ofthe segmented rolls for carrying out liquid core reduction. The distancethe cast slab passes in a time period from the maximum bulgingdeformation t the elimination of the bulging deformation is also equalto the length L_(S).

It is noted from FIG. 10 that the bulging deformation occurs at an exitroll of the segmented rolls (the 5th roll R₅ of FIG. 7 in the case ofFIG. 10) at the time when a clearance is formed between a roll and thecast slab. Until the bulging deformation reaches a maximum value, theclearance is formed at roll 4 (R₄), roll 3 (R₃), and roll 2 (R₂)successively, corresponding to points 04, 03, and 02 in FIG. 10, forexample, and the bulging deformation increases. After reaching a maximumlevel, the clearance disappears gradually while the cast slab passesfrom roll 2 (R₂) through roll 5 (R₅) successively when the roll gap isequal to the thickness of the slab at its edge portions. See points C2,C3, C4, and C5 of FIG. 10.

FIG. 11 shows the change in the shape of a cast slab when a portion ofthe slab where the maximum bulging deformation occurs at the exit of thesegmented rolls is passing through the segmented rolls. In FIG. 11, thearea of interest is cross-hatched. It is to be noted that FIG. 11 doesnot illustrate an exact pass line of the segmented rolls, butillustrates a relative position between a solidified shell at thewidthwise central portion of the slab and supporting rolls so as toclearly explain occurrence of bulging rand roll reduction of the portionwhere the bulging occurs.

Since the distance over which the cast slab passes during the timeperiod from the generation of bulging deformation to attainment of themaximum level thereof is equal to the length of a segmented roll group,contact of the cast slab with rolls is as shown in FIG. 11a when thenoted portion 47 of the cast slab is located at the inlet of thesegmented group of rolls. This situation corresponds to that indicatedby point 05 of FIG. 10 where a clearance is first generated between the5th roll (R₅) and the cast slab. When the noted portion 47 is located atthe 2nd roll (R₂), as shown in FIG. 11b, bulging due to formation of theclearance occurs at the 5th roll (R₅). This situation corresponds tothat indicated by point 04 of FIG. 10, and it is at this point when aclearance is first generated at the 4th roll (R₄). Similarly, FIGS. 11bthrough 11e show respective states when the noted portion 47 passes the3rd roll (R₃), the 4th roll (R₄), and the 5th roll (R₅), whichcorrespond to points 03 and 04 and the release finishing point of FIG.10, respectively.

As is apparent from FIGS. 11(a)-11(f), since a clearance is notgenerated at the 1st to the 3rd rolls until the noted portion 47 reachesthe 3rd roll (R₃), bulging due to formation of the clearance does notoccur. When the noted portion 47 reaches the 3rd roll (R₃), sincebulging due to formation of a clearance occurs at the 4th roll (R₄),tensile strains εbm3 (stretching inside the shell due to the bendingforce applied) in the casting direction are introduced at thesolidification interface just below the 3rd roll (R₃). The quantity εbmis called "misalignment strains of the bulging type". When the notedportion 47 reaches the 4th roll (R₄), since further bulging deformationoccurs at the 5th roll (R₅), misalignment strains εbm4 of the bulgingtype are added.

In the process of the present invention, it is necessary to pinch thecast slab with the upper and lower segment frames at a pressurecorresponding to a static iron pressure so as to keep a once-achievedtarget thickness of the cast slab at segments downstream of thesegmented rolls group where reduction of the cast slab having a liquidcore is carried out so as to achieve a target thickness. Thus, when acast slab having bulging deformation such as shown in FIG. 9 reachesnormal segments following the liquid core reduction segment, the bulgingdeformation is again made to disappear by the pressure applied from thesegmented rolls group, and a rectangular sectional shape is restored tothe cast slab. Reduction in this area, as shown in FIG. 11e, addsstrains εsm in the casting direction at the solidification interface inthe noted portion 47 of the cast slab. These strains are called"reduction strains of the leveled segment type" or merely "reductionstrains of the leveled type". The reduction strains of the leveled typeare introduced at the inlet roll 48 of the segment next to the liquidcore reduction segment.

When the sum of misalignment strains of the bulging type and reductionstrains of the leveled type is larger than a critical amount, internalcracks are formed. Since the amount of these strains is proportional tothe amount of bulging, the amount of strains becomes a maximum at theportion where bulging is a maximum. In this respect, the maximum amountof bulging is proportional to the releasing rate of reduction, i.e., theraising rate of the roll, and is inversely proportional to the castingspeed. In order to prevent formation of internal cracks, therefore, itis advisable to control the maximum bulging, i.e., control a releasingrate in such a way that the sum of these strains is smaller than acritical amount at which internal cracks start occurring.

In order to describe the releasing rate quantitatively, the releasingrate will be defined as a speed of raising an exit roll of the segmentedgroups of rolls for carrying out liquid core reduction, i.e., a liquidcore reduction segment. A maximum bulging deformation db (mm) at theportion just below the exit roll of the liquid core reduction segmentwas determined at varied casting speeds Vc (m/min) and releasing ratesV_(R) (mm/S). The results of the determination are shown in FIG. 12.Based on the results, the following relationship can be derived.

    db=18×V.sub.R ×L.sub.S /L.sub.C                (5)

wherein L_(S) stands for a distance between an inlet roll and an exitroll of the liquid core reduction segment, i.e., the length of theliquid core reduction segment.

As is apparent from equation (5), the maximum bulging db at the exit ofthe liquid core reduction segment is not affected by the amount ofrelease of reduction, but is varied depending on the releasing rate, thecasting speed, and the segment length. The amount of bulging becomes amaximum at a midpoint of the reduction releasing operation, as shown inFIG. 10. The portion of the cast slab where the maximum db is formed issubjected, as illustrated in FIGS. 11(a)-11(f), to introduction of themisalignment strains of the bulging type at an area between the 3rd rolland the 4th roll and then to reduction strains of the leveled type atthe next roll.

According to a finite element analysis made by the inventors, themisalignment strains of the bulging type can be described by thefollowing equation:

    εbm=2.74×(D δ/L.sup.2)×100(%)    (6)

The reduction strains of the leveled type can be described as follows:

    εsm=2.66×(D δ/L.sup.2)×100(%)    (7)

wherein:

D: thickness of solidified shell (mm)

δ: amount of bulging

L: roll pitch

In the case shown in FIGS. 11a-11f, the noted portion 47 is subjected tointroduction of the misalignment strains of the bulging type in an areabetween the 3rd roll (R₃) and the 4th roll (R₄). This is because theliquid core reduction segment contains five rolls. When the segmentcontains a different number of rolls, the location of the roll where thenoted portion 47 suffers from misalignment strains of the bulging typeis also changed. However, such a location is not important, sinceinternal cracks are formed when the amount of strains introduced to abrittle area (usually an area of a solid phase ratio of 0.8-0.99) at thesolidification interface of the solidified shell is increased beyond acritical amount. If the strains are repeatedly introduced, the internalcracks are formed at a time when a total amount of the introducedstrains is over the critical amount. The maximum amount of bulging isthe sum of the amounts of bulging deformation which the noted portionreceives at each of the rolls. In addition, the amount of misalignmentstrains of the bulging type is proportional to the amount of bulging. Ateach of the rolls where bulging occurs, the amount of the misalignmentstrains of the bulging type is calculated and summed. The resultingtotal amount is equal to the amount of strains which are introduced byapplying the maximum bulging at one time. The strains caused byreleasing the liquid core reduction (ε_(R) : strains by reductionreleasing) are a total of the strains obtained by calculation using δ ofthe equations (6) and (7) and the maximum bulging db, and can bedescribed by the following equation. ##EQU2##

In order to prevent occurrence of internal cracks, therefore, it isadvisable to suppress the formation of strains caused by reductionreleasing and also strains caused for other reasons, such as bulgingbetween rolls, thermal stresses, and roll reduction due to roll bendingcaused by thermal expansion of rolls, so as to restrict the total amountof these strains to be smaller than the critical amount. The later typeof strains which are caused by reasons other than releasing of theliquid core reduction are inevitably introduced to cast slabs duringusual continuous casting. These strains, therefor, are called "existingstrains" for convenience. The amount of existing strains is changeddepending on the type of casting machines and operating conditions.However, in order to suppress occurrence of internal cracks caused byreleasing of liquid core reduction, or in order to avoid formation ofinternal cracks caused by accidental malfunction of the casting machineduring normal casting without effecting liquid core reduction, castingmachines are designed such that the amount of the existing strains is atmost 50% or less of the critical amount for internal cracks with afactor of safety being 1.4 or more, although the critical amount variesdepending on the type of steel. Thus, if the amount of strains caused byreleasing the liquid core reduction (ε_(R)) is restricted to 50% or lessof the critical amount for internal cracks, the occurrence of internalcracks can successfully be avoided during releasing of the liquid corereduction.

Since the level of strains causing the occurrence of internal cracks fora particular steel, referred to here as critical amount (ε_(CR)), can bedetermined by such a method as described in "Materials & Processes" Vol.1 (1988)p.1229, for example, operating conditions which will not produceinternal cracks can be obtained from equation (8) as follows. ##EQU3##

wherein

V_(R) : Raising speed of the exit roll in a liquid core reduction zone.

V_(C) : casting speed (m/min)

L: minimum roll pitch i.e., minimum distance from one roll to the nextroll (mm)

L_(S) : length of the liquid core reduction zone to give a targetthickness (m)

ε_(Cr) : amount of strains causing internal cracks for steel to be cast(%)

D: maximum solidified shell thickness at the exit of a liquid corereduction roll (mm)

If the roll pitch L (mm) can take different values within the liquidcore reduction area to give a target reduction, it is advisable from theviewpoint of safety to use as a minimum roll pitch a distance from aroll nearest to the meniscus within the liquid core reduction rolls tothe first roll which can provide a target pressure. In addition,although the solidified shell thickness increases slightly in the liquidcore reduction area where a target reduction is achieved, the solidifiedshell thickness t the exit of the liquid core reduction area can beused. The solidified shell thickness can be obtained by calculation ormeasurement. Alternatively, after determining the solidificationcoefficient K based on the results of the calculation and measurement,the shell thickness can be obtained by the following empirical formula:

    D=K√(L.sub.e /V.sub.C)                              (11)

Instead of using Le, which means the distance (m) from the meniscus, thedistance from the meniscus to the final roll in the liquid corereduction area where a target reduction is achieved can be used for thesake of safety. The above method is not affected by a reduction duringliquid core reduction and is effective in a case where releasing iscarried out after a small amount of reduction, i.e., slight reduction.

Although the before-mentioned prevention f the occurrence of internalcracks has been described with reference to segmented groups of rolls,an upper limit of the raising speed of a pair of rolls which are notsegmented can be determined in the same manner.

Since the thickness of cast slabs is small in the continuous castingmethod employing liquid core reduction, and the solidification finishingposition is rather near the meniscus compared with that after release ofreduction, it is possible to advantageously increase production speed byincreasing the casting speed. If such high speed of casting is continuedafter releasing is initiated, the solidification finishing portionshifts outside the machine, resulting in bulging after leaving themachine. Marked deteriorations in inner quality and shape of productsare inevitable. It is necessary, therefore, that the casting speed bewithin a range where the signification finishing position can be keptwithin an area of the casting machine.

EXAMPLE 1

This example specifically shows that control of roll reduction caneasily be done depending on changes of operational conditions during theliquid core reduction operation.

First, progresses of solidification were simulated on the basis ofcalculations for a case where the liquid core reduction as not carriedout. A simulation model was one-dimensional model for a portion of 1/2the thickness of the slab.

The thickness of mold, i.e., thickness of cast slab within the mold was90 mm. The distance of cast slab from a molten metal level within themold was shown with respect to the solidified shell thickness andtemperature in FIGS. 13a and 13b, respectively. According to the resultsthereof, it is possible to determine a roll reduction position, i.e.,reference position, where the thickness of the solidified shell wasequal to a target thickness.

If cooling conditions, such as temperature of a cooling water arechanged, the thickness of the solidified shell is varied even in thesame roll area. In this simulation, since the results are for the 1/2thickness portion, a solidified shell thickness of 45 mm means completesolidification.

Now take an example where a cast slab of 90 mm thick is reduced to athickness of 60 mm, i.e, a roll reduction by 30 mm is carried out.

According to FIG. 13a, at a position of 7 m from the meniscus within themold the thickness of the solidified shell is 30 mm for the half, i.e,60 mm for the whole, and the thickness of liquid core is 90 mm-60 mm=30mm.

Thus, if a reduction with a roll positioned at a distance of 7 m fromthe meniscus is completely carried out, an unsolidified portion of 30 mmthick is squeezed so that the opposing solidified portions are contactedtogether to give a slab having a solidified thickness of 60 mm. Namely,a roll reduction is 30 mm. In this case, therefore, for the reductionrolls upstream of the pivot reduction roll at a distance of 7 m from themeniscus, roll reduction control may be performed, and for the reductionrolls downstream of the pivot reduction roll, pressure control, i.e.,reaction force control may be performed.

Similarly, in the case shown in FIG. 13b, since the thickness of thesolidified portion is 30 mm for the half of the slab and 60 mm for thewhole at a distance of 6 m from the meniscus, for the reduction rollsupstream of the pivot reduction roll at a distance of 6 m from themeniscus, roll reduction control may be performed, and for the reductionrolls downstream by a distance of 6 m, reaction force control may beperformed.

Comparing the cases of FIG. 13a and FIG. 13b, which differ from eachother in the position of the pivot roll where the thickness of a liquidcore is equal to the reduction, it is noted that the roll reductionconditions must be changed.

However, according to the prior art method, in which spacers are used asstoppers to mechanically stop the reduction of rolls to performreduction under a constant reaction force, or in which the reduction ofrolls is performed in a fixed pattern, the following problems occur whenoperational conditions are to be changed.

Namely, when the thickness of an unsolidified portion is small at thereduction roll position of the pivot reduction device, the thickness ofthe solidified shell is larger than the target thickness afterreduction, even if the reduction is performed.

According to the present invention, if an unsolidified portion remainsat z pivot reduction roll which is selected by the automatic positioncontrol (APC) system, segregation can not e eliminated. Therefore it isdesirable that the thickness of an unsolidified portion be substantiallyzero at the pivot reduction roll position.

Based on the calculation f thermal conductivity shown in FIGS. 13a and13b, or based on equation (2), the performance of a cast slab from thebeginning of roll reduction to the end of roll reduction at the pointwhere the thickness of an unsolidified portion is 30 mm, as well aschanged in the thickness of the unsolidified portion (unsolidificationthickness) and that of a solidified portion (solidification thickness)were simulated. The results are shown in FIG. 14.

In this figure, the most suitable roll position which was determined byAPC was in Case B₀ exhibiting a solidification thickness B₀ and anunsolidification thickness B₀. At a first position (a) of the roll towhich APC is applied, the reduction is substantially equal to theunsolidification thickness, and at a finishing position (b), i.e., theroll position of the pivot reduction device, the unsolidificationthickness is zero. If reaction force control is applied to the rollsdownstream of the pivot roll, therefore, the slab thickness does notchange but is 60 mm, a target thickness.

The roll position is unsuitable in Case A. This is the case in which ata first position (a) of the roll to which APC is applied, thesolidification thickness is small. When the roll reduction reaches 30mm, an unsolidified portion still remains. If reaction force control isnot applied to the rolls downstream, as shown in Case B₁, a target slabthickness of 60 mm can be achieved, but an unsolidified portion is beingcooled and solidified, resulting in no elimination of center linesegregation.

In contrast, if reaction force control is applied to rolls downstream,the slab thickness will be 60 mm or less just like the case shown asCase B₂. a pattern of the roll position control (APC) is changed.Changes in roll reduction and reduction pressure are plotted withrespect to time for a final roll to which the roll position control byAPC is applied.

The reaction force during roll reduction can be described as (P_(i) +α).The value of P_(i) can be determined by equation (3) to be about 30kg/cm² in this case. The reaction force (P_(i) +α) rapidly increaseswhen the roll reduction comes to an end. The inventors determined byseparate experiments the pressure to be 32 kg/cm² at which the reactionforce control of rolls downstream is carried out.

i) as is apparent from FIG. 15, when the reaction force increasesrapidly prior to reaching the target reduction, the solidificationthickness is so large that the resulting slab thickness would beexcessively larger than the target one even if the reaction forcecontrol were applied to the rolls downstream.

Therefore, the pattern of roll position control (APC), i.e., the rollpositions to which APC is applied, is shifted upstream, i.e., a newpattern of position control has a sharp gradient, and the reaction forcecontrol is applied to rolls downstream of the roll to which APC controlis applied.

ii) In contrast, when the reaction force does not increase rapidly afterreaching the target reduction, it is decided that the solidificationthickness is too small. Therefore, the roll positions to which APC isapplied are shifted downstream, i.e., a new pattern of position controlhas a sharp gradient, and the reaction force control is applied to rollsdownstream of the roll to which APC control is applied.

In these respects, the roll reduction control and the reaction forcecontrol were carried out in accordance with the manners shown in FIGS. 4and 5.

Thus, according to the present invention, cast slabs having a precisethickness can be produced with center line segregation being effectivelyeliminated.

EXAMPLE 2

In this example, using a casting machine of the bending type (cast slabthickness=90 mm, cast slab width=100 mm, curvature bending radius=3.5 m,straight portion length=1.6 m, and machine length=13 m), cast slabshaving the steel compositions shown in Table 1 were forged in rollerapron zone (2.9-3.86 m from the meniscus) with a roll reduction of 20 mmbeing performed by the liquid core reduction segment shown in FIG. 8.When the roll reduction of 20 mm was released to return to a 90 mm slab,the control process of the present invention was carried out. In thiscontinuous casting machine, the length L_(S) was 760 mm. Since a rollpitch of from the middle of the liquid core reduction segment in thecasting direction to an inlet of the next segment of usual rolls was190-195 mm, the value of L in equation (9) was set to 190 mm in carryingout the present invention.

                  TABLE 1                                                         ______________________________________                                                                        Critical                                         Steel Composition (wt %) Strains                                           Steel   C         P           S       εcr (%)                         ______________________________________                                        A       0.15 ˜ 0.20                                                                       0.015 ˜ 0.02                                                                        0.01 ˜ 0.015                                                                    1.6                                       B 0.15 ˜ 0.20 0.015 ˜ 0.02 <0.01 2.3                              C 0.2 ˜ 0.4 0.015 ˜ 0.02 0.01 ˜ 0.015 1.0                   D 0.4 ˜ 0.9 0.015 ˜ 0.02 0.01 ˜ 0.015 0.8                   E 0.15 ˜ 0.1  0.015 ˜ 0.02 0.01 ˜ 0.015 2.0               ______________________________________                                    

Table 2 shows the results of the present invention together with thoseof comparative examples. In Table 2, Vc stands for a steady castingspeed at which cast slabs having respective steel compositions were castwith a thickness of 90 mm. The casting speed was increased by 20-30%higher than the steady casting speed when the liquid core reduction wasbeing carried out. Occurrence of internal cracks during release of theroll reduction was determined by the development of cracks on thesurface of a specimen which was cut from a central portion of the castslab in the widthwise direction and subjected to sulphur printing anddendrite etching.

In applying the method of the present invention, the solidificationthickness was found by calculation after thoroughly confirming theprecision thereof based on measurements previously obtained.

According to the method of the present invention, there were no internalcracks. However, when the releasing of roll reduction was carried outusing the value of V_(R) which was not satisfied by equation (10), thelength of a non-steady tapered slab was a little short compared withthat in the case of the present invention, but the cast slab sufferedfrom occurrence of internal cracks. Furthermore, in Comparative ExampleNo. 11, the releasing speed satisfied equation (10), but the castingspeed during release of the liquid core reduction was larger than thesteady casting speed for 90 mm thick cast slabs after finishing therelease of reduction. The final solidification position, therefore, waslocated outside the machine and bulging occurred outside the machine,resulting in formation of internal cracks.

                                      TABLE 2                                     __________________________________________________________________________                            Length of                                                 V.sub.C V.sub.R (V.sub.R)cr Equation Tapered Internal                       No. Steel (m/min) (mm/s) (mm/s) (10) Slab (m) Cracks Remarks                __________________________________________________________________________    1   A  4.1 0.60                                                                              0.65                                                                              ◯                                                                      2.9  No cracks                                                                          Invention                                     2 B 4.1 0.90 0.94 ◯ 2.1 at all                                    3 C 3.8 0.35 0.37 ◯ 4.5                                           4 D 3.5 0.25 0.26 ◯ 5.6                                           5 E 5.0 1.05 1.10 ◯ 2.3                                           6 A 4.1 0.70 0.65 X 2.7 Yes Compara-                                          7 B 4.1 1.00 0.94 X 2.0  tive                                                 8 G 3.8 0.42 0.37 X 3.9                                                       9 D 3.5 0.31 0.26 X 4.6                                                       10 E 5.0 1.20 1.10 X 2.0                                                      11 A 4.5* 0.73 0.75 ◯ 2.8                                       __________________________________________________________________________     Note: Higher than normal casting speed for 90 mm thick slabs.            

INDUSTRIAL APPLICABILITY

According to the present invention, control of roll reduction positionas well as reaction force in response to the roll reduction can becarried out. In addition, the thickness of cast slabs can be freelyincreased or decreased with high precision, and cast slabs having auniform inner structure can be obtained with a centrl portion of castslab being free of segregation of impurities. Furthermore, since it ispossible to produce cast slabs having a thickness required forsubsequent hot rolling steps, loads to the hot rolling mills can bereduced markedly, resulting in an increase in productivity.

In addition, since the pivot roll position can be corrected, cast slabshaving a predetermined thickness can be produced with high precision.

Lastly, it is possible to control the reduction position as well as thereduction force without using expensive apparatuses with aservomechanism, so the present invention has advantages with respect toequipment costs.

We claim:
 1. A process for continuously casting a slab, whichcomprises:supplying a cast slab having a liquid core and continuouslywithdrawn from a mold to a plurality of reduction devices arranged intandem, providing a target roll reduction or a target pressure to eachof the reduction devices, performing roll reduction with the target rollreduction and target pressure capable of being achieved for each of thereduction devices, selecting one of the plurality of reduction devicesas a pivot reduction device where the thickness of the solidified shellof the cast slab reaches a target thickness of the cast slab, providinga target roll reduction to the pivot reduction device and each of thereduction devices located upstream of the pivot reduction device, andproviding a target pressure to each of the reduction devices locateddownstream of the pivot reduction device.
 2. A process for continuouslycasting a slab as set forth in claim 1, wherein a thickness of the castslab is increased or decreased after passing through the plurality ofreduction devices as compared with a thickness the slab whencontinuously withdrawn from the mold.
 3. A process for continuouslycasting a slab as set forth in claim 1, further comprising detecting athickness of the cast slab at the exit of the pivot reduction device,detecting a reduction roll position of the pivot reduction device, andshifting the pivot reduction device based on the detected thickness ofthe cast slab at the exit of the pivot reduction device and based on thedetected reduction roll position.
 4. A process for continuously castingslabs as set forth in claim 1, wherein the target roll reduction iscalculated based on a difference between a thickness of the cast slab atthe exit of the mold and the target thickness of the cast slab.
 5. Aprocess for continuously casting slabs as set forth in claim 1, whereinthe slab is composed of steel and the target pressure is calculatedbased on a preset value of the reaction force to the reduction, which isdetermined depending on a composition of the steel slab and depending ona static iron pressure at each of the reduction devices.
 6. A processfor continuously casting a slab as set forth in claim 1, wherein thereduction device comprises a double acting hydraulic cylinder, pressurecontrol valves for adjusting pressure to the hydraulic cylinder, adetector for detecting the roll reduction, and a pressure meter fordetecting applied pressure,in the case of either increasing ordecreasing the thickness of the cast slab, the target pressure and adirection of application of pressure are determined for the pivotreduction device and each reduction device located upstream of the pivotreduction device based on detected results of the detector and anassigned target roll reduction, a degree of opening of said pressurecontrol valve is determined based on the target pressure and a detectedpressure of the pressure meter, the pressure control valve is operatedto achieve the degree of opening and to switch the direction of pressureapplication, and the degree of opening of the pressure control valve isdetermined for each reduction device located downstream of the pivotreduction device based on an assigned target pressure and the detectedresults of the pressure meter, and the pressure control valve isoperated to achieve the predetermined degree of opening.
 7. A processfor continuously casting a slab as set forth in claim 1, wherein acontinuous cast thin slab of steel is produced by applying reduction ofthickness of a cast slab having a liquid core in a roll reduction zone,the roll reduction force is released in such a way that a rate ofincreasing the final roll reduction is satisfied by the followingequation, which determines the target roll reduction, when the thicknessof the cast slab is returned to a thickness smaller than the originalthickness of the cast slab before application of roll reduction:##EQU4## wherein V_(R) : raising rate of the reduction roll (mm/S)V_(o): casting speed (m/min) L: minimum roll pitch (mm) L_(S) : length ofroll reduction zone (m) ε_(Cr) : critical strains of internal cracks ofcast steel (%) D: maximum solidified shell thickness at the exit of aliquid reducing roll (mm).
 8. A process for continuously casting a slabas set forth in claim 1, wherien the reduction device comprises a pairof reduction rolls.
 9. A process for continuously casting a slab as setforth in claim 1, wherein the reduction device comprises a segmentedgroup of a plurality of pairs of rolls.
 10. A continuous castingapparatus in which a cast slab continuously withdrawn from a mold issupplied to a plurality of reduction devices arranged in tandem, atarget oil reduction or target pressure is assigned to each of thereduction devices, and roll reduction of a liquid core with the targetroll/reduction position or target pressure being able to be achieved foreach of the reduction devices is performed, comprising:means forselecting any one of the plurality of reduction devices as a variablepivot reduction device, means for assigning a target roll reduction tothe pivot reduction device and each of the reduction devices upstream ofthe pivot reduction device, means for assigning a target pressure toeach of the reduction devices downstream of the pivot reduction device,means for providing a roll reduction smaller than the thickness of themold based on means for providing a target roll reduction, when a rollreduction is decreased, and means for providing a roll reduction largerthan that being used, based on the means for providing a target rollreduction, when the roll reduction is increased.
 11. A process forcontinuously casting a slab, comprising:supplying a continuously castslab to a plurality of reduction rollers; performing roll reduction withthe plurality of reduction rollers to obtain an outputted cast slabhaving a target thickness; selecting one of the plurality of reductionrollers as a pivot reduction device at which the cast slab has thetarget thickness during said performing of roll reduction; providing atarget roll reduction to the pivot reduction device and at least onereduction roller of the plurality of reduction rollers located upstreamof the pivot reduction device with respect to a conveyance direction ofthe slab; and providing a target pressure to at least one reductionroller of the plurality of reduction rollers located downstream of thepivot reduction device with respect to the conveyance direction of theslab.